Vaidikalaya

MCQ On Number System

Q1. The base of the binary number system is:.
  1. 2
  2. 8
  3. 10
  4. 16

Answer: a, 2

Solution: Binary numbers use only two digits: 0 and 1. Therefore, the base (radix) is 2.

Q2. The base of the octal number system is:.
  1. 2
  2. 8
  3. 10
  4. 16

Answer: b, 8

Solution: Octal system uses digits 0 to 7, so its base is 8.

Q3. The base of the hexadecimal number system is:.
  1. 2
  2. 8
  3. 10
  4. 16

Answer: d, 16

Solution: The hexadecimal number system uses 16 symbols. 0–9 and A(10), B(11), C(12), D(13), E(14), F(15). Since it has 16 unique digits, its base (radix) is 16.

Q4. The hexadecimal number system uses symbols:.
  1. 0–7
  2. 0–9
  3. 0–9 and A–F
  4. 0–9 and A–Z

Answer: c, 0–9 and A–F

Solution: Hexadecimal uses 16 symbols: 0–9, A(10), B(11), C(12), D(13), E(14), F(15).

Q5. Which of the following is NOT a positional number system?.
  1. Binary
  2. Decimal
  3. Roman
  4. Hexadecimal

Answer: c, Roman

Solution: Roman numerals do not depend on position, hence non-positional.

Q6. Convert the following decimal numbers into binary and choose the correct option: 19, 38, 76, 152.
  1. 10011, 100110, 1001100, 10011000
  2. 10011, 100110, 1001100, 10011000
  3. 10011, 100101, 1001100, 10011000
  4. 10011, 100110, 1001010, 10011000

Answer: b, 10011, 100110, 1001100, 10011000

Q7. Convert the following decimal numbers into binary and choose the correct option: 10.625, 5.375, 0.625.
  1. 1010.101, 101.011, 0.101
  2. 1010.011, 101.011, 0.101
  3. 1010.110, 101.101, 0.011
  4. 1011.001, 110.011, 0.110

Answer: a, 1010.101, 101.011, 0.101

Q8. Convert the following decimal numbers into octal: 26, 52, 104, 208.
  1. 32, 64, 150, 320
  2. 32, 64, 150, 330
  3. 31, 65, 140, 320
  4. 33, 64, 150, 320

Answer: a, 32, 64, 150, 320

Q9. Convert the following decimal numbers into octal: 0.1, 13.625, 45.8125.
  1. 0.146, 15.6, 55.65
  2. 0.063, 15.4, 55.64
  3. 0.314, 16.5, 55.66
  4. 0.777, 15.5, 56.65

Answer: a, 0.146, 15.6, 55.65

Q10. Convert the following decimal numbers into hexadecimal: 31, 64, 256, 512.
  1. 1F, 40, 100, 200
  2. 1E, 40, 100, 200
  3. 1F, 3F, FF, 1FF
  4. 20, 40, 100, 200

Answer: a, 1F, 40, 100, 200

Q11. Convert the following decimal numbers into hexadecimal: 13.625, 0.375, 45.8125.
  1. D.6, 0.6, 2D.D
  2. D.A, 0.4, 2D.C
  3. E.4, 0.8, 2E.D
  4. C.A, 0.A, 2C.E

Answer: a, D.6, 0.6, 2D.D

Q12. Convert the following binary numbers into decimal and choose the correct option: 10101, 11111, 100000, 111111.
  1. 21, 30, 32, 63
  2. 21, 31, 32, 63
  3. 20, 31, 31, 62
  4. 22, 31, 32, 64

Answer: b, 21, 31, 32, 63

Q13. Convert the following binary numbers into decimal and choose the correct option: 10.011, 0.101, 1101.101.
  1. 2.375, 0.625, 13.875
  2. 2.25, 0.5, 13.5
  3. 2.5, 0.75, 13.75
  4. 2.625, 0.875, 13.625

Answer: a, 2.375, 0.625, 13.875

Q14. Convert the following binary numbers into octal and choose the correct option: 101011, 111001, 1000000.
  1. 55, 71, 100
  2. 53, 71, 100
  3. 53, 73, 100
  4. 52, 71, 110

Answer: b, 53, 71, 100

Solution:

Group binary digits in 3 from right

  • 101011 -> 101 011 -> 5 3 -> 53
  • 111001 -> 111 001 -> 7 1 -> 71
  • 1000000 -> 001 000 000 -> 100

Q15. Convert the following binary numbers into octal and choose the correct option: 101.011, 1101.101, 111.111.
  1. 5.3, 15.5, 7.7
  2. 5.6, 15.5, 7.7
  3. 5.3, 15.6, 7.6
  4. 5.6, 15.6, 7.7

Answer: a, 5.3, 15.5, 7.7

Solution:

Group 3 bits on both sides of the point.

  • 101.011 -> 101 . 011 -> 5.3
  • 1101.101 -> 001 101 . 101 -> 15.5
  • 111.111 -> 111 . 111 -> 7.7

Q16. Convert the following binary numbers into hexadecimal: 10101111, 11110000, 10000000.
  1. AF, E0, 80
  2. AE, F0, 80
  3. AF, F0, 80
  4. A7, F0, 100

Answer: c, AF, F0, 80

Solution:

Group binary digits in 4 from right

  • 10101111 -> 1010 1111 -> AF
  • 11110000 -> 1111 0000 -> F0
  • 10000000 -> 1000 0000 -> 80

Q17. Convert the following binary numbers into hexadecimal and choose the correct option: 1011.101, 1110.0111, 1001.1111.
  1. B.B, E.7, 9.F
  2. B.A, E.7, 9.F
  3. A.B, E.6, 9.E
  4. B.A, F.7, 9.F

Answer: b, B.A, E.7, 9.F

Solution:

Group 4 bits on both sides.

  • 1011.101 -> 1011 . 1010 -> B.A
  • 1110.0111 -> 1110 . 0111 -> E.7
  • 1001.1111 -> 1001 . 1111 -> 9.F

Q18. Convert the following octal numbers into decimal and choose the correct option: 17, 77, 100, 377.
  1. 15, 63, 64, 255
  2. 14, 63, 64, 255
  3. 15, 64, 63, 256
  4. 16, 63, 64, 254

Answer: a, 15, 63, 64, 255

Solution:

Group 4 bits on both sides.

  • 17 -> 1*81+7*80 -> 8+7 = 15
  • 77 -> 7*81+7*80 -> 56+7 = 63
  • 100 -> 1*82+0*81+0*80 -> 64+0+0 = 64
  • 377 -> 3*82+7*81+7*80 -> 192+56+7 = 255

Q19. Convert the octal number 12.4 into decimal.
  1. 10.25
  2. 10.5
  3. 10.75
  4. 11.25

Answer: b, 10.5

Solution:

12.4 -> 1*81+2*80+4*8-1 -> 10+0.5 = 10.5

Q20. Convert the following octal numbers into binary: 25, 64, 157.
  1. 10101, 110100, 1101111
  2. 10011, 110100, 1101111
  3. 10101, 110010, 1101111
  4. 10101, 110100, 1110111

Answer: a, 10101, 110100, 1101111

Solution:

  • 25? -> 010 101 -> 10101
  • 64? -> 110 100 -> 110100
  • 157? -> 001 101 111 -> 1101111

Q21. Convert the octal number 15.6 into binary.
  1. 1101.11
  2. 1101.101
  3. 1110.11
  4. 1101.011

Answer: a, 1101.11

Solution:

15.6? -> 001 101 . 110 = 1101.110

Q22. Convert the following hexadecimal numbers into decimal and choose the correct option: 1A, 3F, 80, FF.
  1. 26, 63, 128, 255
  2. 25, 63, 128, 255
  3. 26, 62, 128, 254
  4. 27, 63, 127, 255

Answer: a, 26, 63, 128, 255

Solution:

  • 1A -> 1*161+A*160 -> 16+A(10) = 26
  • 3F -> 3*161+F*160 -> 48+F(15) = 63
  • 80 -> 8*161+0*160 -> 128+0 = 128
  • FF -> F*161+F*160 -> 240+15 = 255

Q23. Convert the hexadecimal number A.8 into decimal.
  1. 10.25
  2. 10.5
  3. 10.75
  4. 11.5

Answer: b, 10.5

Solution:

A.8?? = 10 + (8×1/16) = 10+0.5 = 10.5

Q24. Convert the following hexadecimal numbers into binary: A5, 3C, F0.
  1. 10100101, 00111100, 11110000
  2. 10100101, 00111000, 11110000
  3. 10110101, 00111100, 11100000
  4. 10100101, 00111110, 11110000

Answer: a, 10100101, 00111100, 11110000

Solution:

  • A5?? -> 1010 0101 = 10100101
  • 3C?? -> 0011 1100 = 00111100
  • F0?? -> 1111 0000 = 11110000

Q25. Convert the hexadecimal number B.6 into binary.
  1. 1011.011
  2. 1011.011
  3. 1101.011
  4. 1011.11

Answer: a, 1011.011

Solution:

B.6 = 1011 0110 = 1011.0110